Part I of this two-paper series presents closed-form analytical expressions for the two-phase emergency relief requirements of top-vented vertical cylindrical containers when the fluids involved exhibit partial disengagement. Both churn-turbulent flow and bubbly flow fluid behaviors, with disengagement parameters greater than unity, are considered. Energy input from either runaway reactions or uncontrolled external beat is included. The methods are limited to systems that are tempered and do not contain noncondensable components. In Part II, the models developed in Part I are applied to specific points along the venting transient, yielding expressions for the required flowrate under emergency conditions. Part H elaborates on the limitations of the models, illustrates the use of the models with numerical examples, and compares the results against previous work. The effect of disengagement parameters greater than unity is illustrated in terms of both the required relieving rate and the mass remaining inside the container when disengagement occurs. (C) 2004 American Institute of Chemical Engineers.